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Kay [80]
3 years ago
5

Which expression below gives the average rate of change of the function g(x) = -x^2 - 4x on the interval 6 ≤ x ≤ 8 ?

Mathematics
2 answers:
Katyanochek1 [597]3 years ago
4 0

Answer:

1st Option

Step-by-step explanation:

Average rate of change formula: \frac{f(a) - f(b)}{a-b}

Simply plug in 8 as a and 6 as b.

Gnesinka [82]3 years ago
3 0

Answer:

A.

Step-by-step explanation:

Δy /Δx = (y2 - y1)/(x2 - x1) = [g(x2) - g(x1)]/(x2 - x1)

[g(x2) - g(x1)]/(x2 - x1) =[g(8) - g(6)]/(8 - 6) =\frac{[-8^{2}-4(8)]-[-6^{2}-4(6)]}{8-6}

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1) Find the graph of a line passing through (-1, 4) and (2, 0).

The slope of two points can be determined by dividing the difference of y-values by the difference of x-values:

\frac{4-0}{-1-2} =\frac{4}{-3}

The slope of this equation is -4/3. Inputting this into the slope-intercept form of an equation, we get:

y=\frac{-4}{3} x+b

To find b, substitute x and y for one of the given coordinate pairs:

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Substitute the b value into the equation to finish the line:

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Anvisha [2.4K]

Answer:

y''(-1) =8

General Formulas and Concepts:

<u>Pre-Algebra</u>

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  4. Multiplication
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Equality Properties

<u>Algebra I</u>

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The derivative of a constant is equal to 0

Basic Power Rule:

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Product Rule: \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

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Step-by-step explanation:

<u>Step 1: Define</u>

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

<u>Step 2: Differentiate Pt. 1</u>

<em>Find 1st Derivative</em>

  1. Implicit Differentiation [Product Rule/Basic Power Rule]:                            -y - xy' - 2y' = 0
  2. [Algebra] Isolate <em>y'</em> terms:                                                                               -xy' - 2y' = y
  3. [Algebra] Factor <em>y'</em>:                                                                                       y'(-x - 2) = y
  4. [Algebra] Isolate <em>y'</em>:                                                                                         y' = \frac{y}{-x-2}
  5. [Algebra] Rewrite:                                                                                           y' = \frac{-y}{x+2}

<u>Step 3: Find </u><em><u>y</u></em>

  1. Define equation:                    -xy - 2y = -4
  2. Factor <em>y</em>:                                 y(-x - 2) = -4
  3. Isolate <em>y</em>:                                 y = \frac{-4}{-x-2}
  4. Simplify:                                 y = \frac{4}{x+2}

<u>Step 4: Rewrite 1st Derivative</u>

  1. [Algebra] Substitute in <em>y</em>:                                                                               y' = \frac{-\frac{4}{x+2} }{x+2}
  2. [Algebra] Simplify:                                                                                         y' = \frac{-4}{(x+2)^2}

<u>Step 5: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

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  2. [Derivative] Simplify:                                                                                      y'' = \frac{8}{(x+2)^3}

<u>Step 6: Find Slope at Given Point</u>

  1. [Algebra] Substitute in <em>x</em>:                                                                               y''(-1) = \frac{8}{(-1+2)^3}
  2. [Algebra] Evaluate:                                                                                       y''(-1) =8
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